As in the title, Quality Module 1 just finished researching and now the game is non-responsive. I've let it just do its thing for about five minutes now, but it's full-on frozen still.

I removed some mods and when the research completed it didn't hang this time.
The mods in question were more walls and filter chests, not sure what interaction caused it to freeze.

I can't seem to find "more walls". But it definitely could be a massive amount of items. You could set those items to NoQuality in the options.

Ah, my bad. It was Reinforced Walls: https://mods.factorio.com/mod/Reinforced-Walls

I have Filter Chests, Reinforced Walls and JQ installed. Researched quality module 1 and it worked fine.

If you have a save file that could help.

Unfortunately I don't.
It hung permanently again when I researched Quality Module 2, so it's probably just a bulk thing.

I disabled a few more mods such as Fluid Permutations, which probably added a tonne of recipes to the list, and now while it hitches it doesn't hang indefinitely.

I got it to do it again, this time upon researching Quality Module 3. How do I upload a save?

Okay, I can definitely confirm it's either a bulk thing or some sort of script interaction (for this save):
With Fluid Permutations active, the game completely locks up.
Deactivating Fluid Permutations before the research finishes, the game barely pauses.
REactivating Fluid Permutations after the research finishes, the game is still fine.

Fluid permutations adds a ton of recipes. Researching quality modules causes a lot of recipes to be unlocked. There's an issue in the game engine (to be fixed in 2.0) with furnace recipes which makes unlocking them very slow.

If you want a 2.0-ish experience, consider setting Fluid permutations to "simple mode" which only creates reversed ingredients rather than full permutations.

It seems it's something script related. Even with FP set to simple, it hangs for me. Swapping to GDIW completely solved the issue.